I have a 1965 Cadillac Coupe DeVille, The battery is 850 CCA and is less than 3 weeks old. my Alternator light stays on and starts to dim when I press on gas.

I had the alternator tested twice by two different auto parts stores.
I installed a new regulator (part number is correct)
I checked all regulator and alternator contacts(lubed w/dielectric grease, checked wire connections and all grounds but still no luck in the battery charging.
Any Ideas?
Also what is a field wire? Someone said that the alternator works based on the reading given by the field wire. I have no idea what this is.
What I do know is there are two posts on the alternator and a plug in the back.
The plug is connected and goes to the regulator
The pigtail is going to the battery and another wire on the positive post, I don't recall but I think it goes down to the starter.
And then there's the ground post which is grounded.
You can do the best by checking the charging system running instead of just the alternator out of the car.
I don't think there is a dead cell on the battery because it's less than 3 weeks old, it's unlikely but possible I'll check the water level tomorrow.
Any help would be greatly appreciated! Thanks!